Related papers: Self-force: Computational Strategies
Attention mechanisms, and most prominently self-attention, are a powerful building block for processing not only text but also images. These provide a parameter efficient method for aggregating inputs. We focus on self-attention in vision…
This paper focuses on regularisation methods using models up to the third order to search for up to second-order critical points of a finite-sum minimisation problem. The variant presented belongs to the framework of [3]: it employs random…
We numerically calculate the dissipative part of the self-force on a scalar charge moving on a circular, geodesic, equatorial orbit in Kerr spacetime. The solution to the scalar field equation is computed by separating variables and is…
The self field of a charged particle has a component that diverges at the particle. We use both coordinate and covariant approaches to compute an expansion of this singular field for generic geodesic orbits in Schwarzschild spacetime for…
We calculate the self-force acting on a particle with scalar charge moving on a generic geodesic around a Schwarzschild black hole. This calculation requires an accurate computation of the retarded scalar field produced by the moving…
Stationary solution of one-dimensional Sine-Gordon system is embedded in a multidimensional theory with explicitly finite domain in the added spatial dimensions. Semiclassical corrections to energy are calculated for static kink solution…
Discrete mechanics is used to present fluid mechanics, fluid-structure interactions, electromagnetism and optical physics in a coherent theoretical and numerical approach. Acceleration considered as an absolute quantity is written as a sum…
This review is concerned with the motion of a point scalar charge, a point electric charge, and a point mass in a specified background spacetime. In each of the three cases the particle produces a field that behaves as outgoing radiation in…
We present a comprehensive method for the evaluation of a vast class of integrals representing 3-point functions of conformal field theories in momentum space. The method leads to analytic, closed-form expressions for all scalar and…
Point processes are stochastic models generating interacting points or events in time, space, etc. Among characteristics of these models, first-order intensity and conditional intensity functions are often considered. We focus on…
In this paper, we propose a methodology designed to support decision-making during the execution phase of military ground combat operations, with a focus on one's actions. This methodology generates and evaluates recommendations for various…
This work introduces a Hamiltonian approach to regularization and linearization of central-force particle dynamics through a new canonical extension of the so-called "projective decomposition". The regularization scheme is formulated within…
Through detection by low gravitational wave space interferometers, the capture of stars by supermassive black holes will constitute a giant step forward in the understanding of gravitation in strong field. The impact of the perturbations on…
This work aims to provide standard formulations for direct minimization approaches on various types of static problems of continuum mechanics. Particularly, form-finding problems of tension structures are discussed in the first half and the…
While approaches to model the progression of fracture have received significant attention, methods to find the solution to the associated nonlinear equations have not. In general, nonlinear solution methods and optimization methods have a…
Using the mathematical theory of shape calculus as tool, we perform a rigorous investigation of the virtual work principle for the computation of electromagnetic forces in static settings. The main goal is to shed light on the widely held…
A finite-element algorithm for computing free-surface flows driven by arbitrary body forces is presented. The algorithm is primarily designed for the microfluidic parameter range where (i) the Reynolds number is small and (ii) force-driven…
Several construction methods for rational approximations to functions of one real variable are described in the present paper; the computational results that characterize the comparative accuracy of these methods are presented; an effect of…
The $\xi$-based spatially adaptive three-field variable phase-field model for quasi-static anti-plane crack propagation is introduced. A dynamically optimized regularization length is integrated to improve computational efficiency and…
Inverse reinforcement learning (IRL) is computationally challenging, with common approaches requiring the solution of multiple reinforcement learning (RL) sub-problems. This work motivates the use of potential-based reward shaping to reduce…